Tomo-Net: A Physics-Inspired Dual Regression Network for Nonlinear Tomographic Imaging

Linear models are extensively employed in tomographic imaging to model the imaging system, with tomographic reconstruction from measurement data typically formulated as a linear inverse problem. However, linear models fail to accurately characterize the imaging system under nonideal imaging conditions. Nonlinear models provide a superior characterization of tomographic imaging systems in such conditions, albeit posing substantial challenges in directly solving the associated nonlinear inverse problem. This article introduces a physics-inspired dual regression network (Tomo-Net), which integrates dual learning with the physical mechanisms of tomographic imaging to solve the nonlinear inverse problem. Tomo-Net constructs a dual regression network by incorporating both primal and dual mappings. Primal mapping facilitates the transformation of degraded measurement data into high-quality reconstructed images, while dual mapping enables the transformation of reconstructed images back to the original measurement data. Tomo-Net incorporates the physical mechanisms of tomographic imaging in both mappings to constrain the solution of the nonlinear inverse problem, and solves the issue of nonuniqueness in the solution space by enforcing data fidelity constraints, dual cycle consistency constraints, and physical mechanism consistency constraints. In addition, Tomo-Net applies consistency constraints during the training phase rather than inference, thereby avoiding additional inference costs. While adaptable to various imaging modalities with suitable modifications, this article focuses on X-ray computed tomography (CT) imaging as a specific example and evaluates its effectiveness across various reconstruction tasks. The extensive experimental results demonstrate that Tomo-Net outperforms traditional machine learning models in solving nonlinear inverse problems in CT. The Tomo-Net code is publicly available at https://github.com/guoyii/Tomo-Net.